The research work dealing with the bi-level formulation of location problems is limited only to the competition among the locators, that is, it is supposed that either both the locator and the allocator are the same or the customer knows the optimality criterion of the locator and agrees passively with it. Customers’ preferences as well as externalities (such as road congestion, facility congestion, emissions etc) caused by the location decisions are either ignored or controlled by incorporating constraints in order to ensure the achievement of a predetermined target. However, this approach treats customers as irresolute beings. Thus, if, for example, the customers travel to the facilities to obtain the offered service, then there is no compulsion or intensive for them to attend the designated facility. This means that, once the facilities are open, what the locator wishes the customers to do may not coincide with their own wish and behavior. We suppose that the customers are involved in a Nash game in order to ensure what they conceive as the best level of services for themselves. In order to take into consideration the effects of such competition in the facilities location decisions we propose a bi-level programming approach to the problem.

Many problems in supply chain optimization concern the minimization of a differentiable convex objective function subject to a set of linear constraints. The aim of this work is to present a number of such problems and to propose an efficient method for their solution. The proposed method is based on improvements of the well known Frank–Wolfe algorithm. The computational results of the proposed algorithm demonstrate its effectiveness and efficiency

The research work dealing with the competitive location problems is limited only to the competition among the locators, that is, it is supposed that either both the locator and the allocator are the same or the customer knows the optimality criterion of the locator and agrees passively with it. Customers preferences as well as externalities (such as road congestion, facility congestion, emissions, etc.) caused by the location decisions are either ignored or “controlled” by incorporating constraints in order to “ensure” the achievement of a predetermined target. However, this approach treats customers as irresolute beings. Thus, if, for example, the customers travel to the facilities to obtain the offered service, then there is no compulsion or incentive for them to attend the designated facility. This means that, once the facilities are open, what the locator wishes the customers to do may not coincide with their own wish and behavior.

The research work dealing with the bi-level formulation of location problems is limited only to the competition among the locators, that is it is supposed that either both the locator and the allocator are the same or the customer (i.e., the user as a whole) knows the optimality criterion of the locator and agrees assively with it. Customers' preferences as well as externalities (such as roadcongestion, facility congestion, emissions etc) caused by the location decisions are either ignored or controlled by incorporating constraints in order to ensure the achievement of a predetermined target. However, this approach treats customers as irresolute beings. Thus, if, for example, the customers travel to the facilities to obtain the offered service, then there is no compulsion or intensive for them to attend the designated facility. This means that, once the facilities are open, what the locator wishes the customers to do may not coincide with their own wish and behavior. We suppose that the customers are involved in a Nash game in order to ensure what they conceive as the best level of services for themselves. In order to take into consideration the effects of such competition in the facilities location decisions we propose a bi-level programming approach to the problem.

Competitive facility location problems are concerned with the following situation: a firm wants to locate a predefined number of facilities to serve customers located in some region where there already exist (or will be) other firms offering the same service. Both new and existing firms compete for optimizing their market share of profit. A discrete version of such problems arises when it is assumed that there are a (rather small) finite number of candidate locations and the markets consist of point demands. We review modeling and optimization approaches for this type of problems and we emphasize and develop the bi-level programming methodology.

In this study we investigate a two-part tariff licensing contract that enables an incumbent innovator to license a cost reducing innovation in a Cournot duopoly characterized by non-

During June 15–20, 2014, a group of scientists gathered together in a conferenceon “Optimization, Control and Applications in the Information Age” in order tocelebrate and honor Panos M. Pardalos on the occasion of his 60th birthday. Themeeting took place at theMeliton Hotel of Porto Carras on the middle leg (Sithonia)of the Chalkidiki peninsula in Macedonia, northern Greece, a place of exquisitebeauty and one of Panos’s favorite places. The conference was organized by SergiyButenko and Athanasios Migdalas and was attended by scientists from all over theworld. More than 50 members of this “Panos’s club” presented talks during thisevent.This volume is dedicated to Panos M. Pardalos, on the occasion of his 60thbirthday. The articles collected in this volume are based on selected talks presentedduring the conference. Several members of the Panos’s club could not attendconference, but have submitted their papers to this volume in order to honor him.The papers published in this volume cover a wide range of topics and presentrecent developments and surveys in research fields to which Pardalos has activelycontributed and promoted during his career.In addition, Panos’s spouse, Rosemary Bakker, has written a brief biographydescribing Panos’s exciting journey from a pastoral village on the high mountainsin Thessaly, central Greece, to a Distinguished Professorship at the University ofFlorida, that is, Panos’s own Odyssey. We therefore dedicate to him the first versesof Homer’s Odyssey and Cavaphes’ poem “Ithaka” believing that they accuratelydescribe Panos’s past, his present, and his future discovery voyages.We are indebted to Springer publishers and particularly to Razia Amzad for theirsupport in making the publication of this volume possible.

The formalization of this class of problem and the fundamental complexity results were established by Hakimi [28]. Following the game introduced by von Stackelberg [76], Hakimi [28] presented the two basic problems in sequential location analysis, the centroid and medianoid problems. These two problems are faced by the leader and the follower, respectively. The leader attempts to locate p( ≥ 1) facilities knowing that a follower will in turn locate his r( ≥ 1) facilities based on the leader’s chosen locations; this is the (r | p)-centroid problem. The follower knows the set X p that indicates where the leader’s facilities are located, and solves an (r | X p )-medianoid problem. Customers choose among the facilities according to a function of the distance between themselves and the facilities, preferring always the closest. This is the so-called binary customer choice. The formulation of the problems is based on the assumption that co-location is not allowed and if, by any chance the distance from a customer to the closest facility of the two competitors is the same, the customer always prefers the leader’s facility. The demand of the customer is also considered to be inelastic with respect to the distance traveled.